Only using smooth continuous changes , Reidemeister's
moves, ( one
- two
- three)
with
no
rethreading, no cutting, no gluing, give it the appearance of the
other.
By doing that you will show that they are "equivalent".
You can try to use this more recent aspect of the Perko pair
instead of the first given one.
They
are said "the PERKO pair" after the name of the astute person who shown
that
they
were *not* two distinct knots ; just a someone seen in full face and
the same someone
seen in
profile are not distinct individuals.
A
FIXED LOOP IS EQUIVALENT TO A SLIPPING LOOP
or
BOWLINE
(considered to be a fixed loop) TRANSMOGRIFIED INTO A NOOSE Do
not open this link at the moment but 'rope in
hands' try
to find how
you would
proceed
to get a
noose / sliding loop with a bowline.
I very much doubt that a loaded bowline could have this
behaviour, it
still remain that it is
easy to do it with a bowline in a *very
relaxed* 'setting'.
Using 'le noeud de chaise
préparé' / the prepared bowline (#1788), some of the time you
may
get this
result without even trying!
So please, just as while scuba diving one must always
verify that one's action has the
intended result with the environment
as
reference, when making a bowline 'prepared"
carefully verify the
resulting knot before putting it into use.
Conclusion
:
BEWARE of "written in stone" classification and of the
"admitted
idea that every one know": a fixed loop is sometime (equivalent to) a slipping
loop or noose and that
without
any rethreading of the knot ! just a question of "arranging,
dressing it'.
JUST
BY SUBTLY MODIFYING ( wantonly or inadvertently) # 1788 GET A
LAP/LAPP
BOWLINE OR AN OUTSIDE TAIL Bwl INSTEAD OF THE USUAL
INSIDE TAIL ONE.
Look at ABoK
#1788, this is what is named here in France "le noeud de
chaise
préparé"
in other words 'the prepared Bwl'
Subtly change either crossing(s) and/or the way the WEnd (
Working End) is thread in so
as to get the 2
other types
